Model Theory

The goal of the lecture is to use the proof of Morley's categoricity theorem to show various techniques in modern model theory. The topics covered will include definable sets, saturated models, prime models, Morley's rank, stability, categoricity and others.

The following links to an expanded syllabus. For the exam I will not require you to know the proofs of theorems which are accompanied by the note 'without proof'. The numbers in parenthesis refer to the book Marcja, Toffalori: A Guide to Classical and Modern Model Theory, if they are preceded by a capital H, they refer to the book Hodges: A Shorter Model Theory. The syllabus may contain mistakes for which I apologize. However these mistakes are not a valid excuse during the exam. If you are not sure about something, ask during the lectures.

References

  • W. Hodges, A Shorter Model Theory, CUP 2003
  • C. C. Chang and H. J. Keisler, Model Theory, North-Holland 1973
  • A. Marcja, C. Toffalori, A Guide to Classical and Modern Model Theory, Kluwer 2003